Fixed points of Bregman relatively nonexpansive mappings and solutions of variational inequality problems

Volume 9, Issue 5, pp 2541--2552 http://dx.doi.org/10.22436/jnsa.009.05.52

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Authors

Mohammed Ali Alghamdi - Operator Theory and Applications Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia. Naseer Shahzad - Operator Theory and Applications Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia. Habtu Zegeye - Department of Mathematics, University of Botswana, Pvt. Bag 00704 Gaborone, Botswana.

Abstract

In this paper, we propose an iterative scheme for finding a common point of the fixed point set of a Bregman relatively nonexpansive mapping and the solution set of a variational inequality problem for a continuous monotone mapping. We prove a strong convergence theorem for the sequences produced by the method. Our results improve and generalize various recent results.

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Keywords

• Bregman distance function
• Bregman relatively nonexpansive mapping
• fixed points of mappings
• strong convergence
• monotone mapping.

MSC

•  47H05
•  47H09
•  47J25
•  49J40

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